Move vanity location and far away from plumbing

I would rethink your bathroom design. A large vanity may not be your best option given the size of the room, toilet proximity, etc.

You may want to consider a corner pedestal and an upright shelving/drawer system instead. Lots of options other than a long vanity with semi-blocked drawers.

Staying closer to the original plumbing outlets make plumbing concerns simpler, less expensive and more likely to work well.

People often choose a vanity over a pedestal sink because of storage and counter space. Ultimately, a vanity is a large piece of furniture going into a relatively small space. If you use a 48” vanity it is a better fit but it still takes up more floor room than a corner pedestal and shelving/cabinet option and requires more plumbing modifications.

Your concern about the sink being so close to the toilet is noted. With a corner install, the sink is away from toilet (nearly as much as with a 48” vanity), and creates much more actual and visual floor and wall space for a less crowded feeling. A corner med cab can be installed as well to provide storage.

I offer these suggestions based on my years of bathroom remodels.

You need to have a clearance between vanity and toilet of 15" measured from the center of the toilet towards the side

You can relocate the plumbing toward the left side of the wall and install the vanity sink there. You can have the drawers on the opposite side to make possible to have them open